The expression given is,
[tex]-\frac{21r^5}{28r^4}=-\frac{3r}{4}[/tex]
To prove if the left-hand side is equal to the right-hand side, we will reduce the left-hand side expression to its lowest term.
The left-hand side expression is,
[tex]-\frac{21r^5}{28r^4}[/tex]
Factor the number 21 :
[tex]\begin{gathered} 21=7\times3 \\ =-\frac{7\times\: 3r^5}{28r^4} \end{gathered}[/tex]
Factor the number 28:
[tex]\begin{gathered} 28=7\times4 \\ =-\frac{7\times\: 3r^5}{7\times\: 4r^4} \end{gathered}[/tex]
Cancel the common factor 7:
[tex]=-\frac{3r^5}{4r^4}[/tex]
Simplify
[tex]\begin{gathered} \frac{r^5}{r^4}\frac{=r^4\times r}{r^4}=r \\ \therefore\frac{r^5}{r^4}=r \end{gathered}[/tex]
Therefore,
[tex]-\frac{3r^5}{4r^4}=-\frac{3r}{4}[/tex]
Now comparing both the right-hand side and the left-hand side, we can see that both are the same.
Hence, the answer is TRUE.
